The present invention relates generally to noise filters, and more particularly, to a matched-phase noise filter and associated method which enables a signal which is extremely weak relative to associated noise to be extracted from an extremely noisy channel.
Presently available methods for enhancing the signal-to-noise ratio (SNR) of a noisy recording include, in increasing order of sophistication, bandpass filtering, optimal filtering, averaging, and noise subtraction. Bandpass filtering is effective when the signal and the noise are known to occupy different portions of the frequency spectrum, with the pass band(s) being set to allow passage of the signal and to reject the noise. Optimal filtering (which is a generalization of bandpass filtering) is effective to improve the SNR when the frequency spectrum of the signal is known, with the shape of the filter frequency curve being set to match that of the original spectrum. With the averaging approach, many recordings of the same signal received at different times are averaged. Presumably, the noise in the overlaid recordings is canceled by the mechanism of destructive interference, while the signal is obtained by the mechanism of constructive interference. With this approach, it is necessary to accurately detect a timing mark within the signal time series in order to obtain constructive signal interference among the different recordings. The signal processing gain for this approach is equal to the number of independent recordings averaged. The noise subtraction approach can be utilized when a precise recording of the noise field is made simultaneously with the reception and recording of the noisy signal. With this approach, the noise time series is subtracted from the recording containing the noisy signal to thereby yield a xe2x80x9ccleanxe2x80x9d signal with the noise removed therefrom. An illustrative example of a device which employs this technique in the field of law enforcement works in the below-described manner. First, a conversation between criminal suspects is deliberately obscured by increasing the volume on a nearby radio or television, and law enforcement personnel recording the obscured conversation simultaneously make a xe2x80x9ccleanxe2x80x9d recording of the same radio or television program at another location. The xe2x80x9ccleanxe2x80x9d recording of the xe2x80x9cnoisexe2x80x9d signal (i.e., the recorded radio or television program) is later subtracted from a recording of the obscured conversation, thereby yielding a xe2x80x9ccleanxe2x80x9d signal which can be made to reveal the content of the conversation.
Although the first three noise filtering techniques are adequate for many applications, they each attempt to recover a signal from a noisy background by recognizing features of the signal (i.e., by its expected time signature or spectral domain), and thus, in addition to other limitations and shortcomings, are ineffective when no a prior information about the received signal is available. The final technique, in contrast, becomes ineffective unless a pure recording of the xe2x80x9cnoisexe2x80x9d is available at precisely the time of interest.
In the past, attempts were made to suppress noise in cases in which the strength of the signal is extremely weak relative to that of the noise by utilization of such array processing techniques as matched-field processing and beam forming, which typically exploit the spatial structure of the acoustic field through multiple sensors to effect a gain. Thus, these array processing techniques are also ineffective in systems in which a single phone or sensor, whether moving or stationary, is available. Furthermore, the presently available signal processing techniques do not make full use of all that is known about a background noise field in order to improve the SNRs. For example, the Heard Island Feasibility Test disclosed in an article entitled xe2x80x9cThe Heard Island Feasibility Testxe2x80x9d, J. Acoust. Soc. Am. 96, 2343-2352 (1994), averaged many receptions of a repeatedly transmitted sequence as part of a xe2x80x9cpulse compressionxe2x80x9d strategy in order to improve SNR. This strategy relies on being able to align receptions of carefully coded signal segments before averaging them together, achieving gain by virtue of the vanishing long-term time average of the noise field. No attempt was made to xe2x80x9crecognizexe2x80x9d the noise field by its spectral profile, and thus use the knowledge of what noise xe2x80x9csounds likexe2x80x9d in order to reject it.
Based on the above, it can be appreciated that there presently exists a need in the art for a noise filtering method (and noise filter for implementing the same) which improves signal-to-noise ratios (SNRs) in noise dominated data, utilizing information concerning the shape of the noise spectrum, even in cases of very-low-signal-to-noise-ratio (VLSNR) where no a priori information about the signal is known, and no a priori information about the phase of the noise field is known. The present invention fulfills this need in the art.
Accordingly, an overall object of the present invention is to improve the signal-to-noise ratio (SNR) of a noise-dominated recording made on a single receiver (as opposed to an array) by removing the majority of the noise, which signal component is recognized by the shape of its power spectrum.
An object according to the present invention is to provide an acoustic filter which permits the use of the known shape of the noise spectrum for purposes of noise rejection without a priori knowledge of the relative phases of the different frequency components of the noise itself. NO a priori knowledge of the signal is required. More specifically, when a signal of interest and noise are completely un-correlated the performance of the present invention is maximized.
Another object according to the present invention is to provide a signal processing algorithm for suppressing noise in cases for which the strength of the signal is extremely weak relative to that of the noise. According to one aspect of the algorithm, unlike many signal processing methods (e.g., matched-field processing, beam forming, or other array processing techniques, which typically exploit the spatial structure of the acoustic field through multiple sensors to effect a gain) the algorithm according to the present invention concentrates on the noise content of a recording from a single phone or sensor whether moving or stationary. Consequently, it offers performance enhancement for work using only a single phone such as single-phone localization, as well as multiple-phone array processing.
Yet another object according to the present invention is to provide a method for extracting more information per sensor by using the physical characteristics of the noise field ascertainable from the collected data. The form of this a priori knowledge could in principle be extended to any measurable quantity, but the algorithm is most effective for those cases where the frequency spectrum of the noise field is known approximately. This is a natural choice, since frequency spectrum measurements and/or models of all types of sources (both discrete and ambient) are quite common in the literature. Furthermore, it has been shown recently, for example, that the shape of the underwater noise spectrum from wave breaking may be estimated from properties of the observable ocean surface wave field, thus offering the possibility of incorporating knowledge about the noise spectrum implicitly derived from observations unrelated to direct acoustic measurements.
The method according to the present invention enhances signal detection in cases of very-low-signal-to-noise ration (VLSNR) when the shape of the noise spectrum is known, but all relative phase information of individual frequency components is unknown. The method also has the advantage of being easy to implement.
Many contemporary signal processing strategies do not make full use of all that is known about a background noise field in order to improve SNRs. For example, no attempt is made to xe2x80x9crecognizexe2x80x9d the noise field by its spectral profile, and thus use the knowledge of what noise xe2x80x9csounds likexe2x80x9d in order to reject it.
Other approaches from simple bandpass filters to more sophisticated optimal filters attempt to recover a signal from a noisy background by recognizing features of the signal (i.e., by its expected time signature or spectral domain). In contrast, the method according to the present invention advantageously uses unknown phases of the noise field plus a single amplitude coefficient to construct a realization of the noise which, when subtracted from the given time series, best quiets the data.
These and other objects, features and advantages according to the present invention are provided by a matched-phase noise filter including a processor implementing the filter function:                     F        ~            ⁡              (        ω        )              =                  ⅇ                              +            1                    ⁢                      xe2x80x83                    ⁢          φ          ⁢                      xe2x80x83                    ⁢                      (            ω            )                              (                        "LeftBracketingBar"                                    P              ~                        ⁡                          (              ω              )                                "RightBracketingBar"                -                                            ∫                              xe2x80x83                            ⁢                                                ⅆ                  ω                                ⁢                                  "LeftBracketingBar"                                                                                    P                        ~                                            ⁡                                              (                        ω                        )                                                              ||                                                                  N                        ~                                            ⁡                                              (                        ω                        )                                                                              "RightBracketingBar"                                "AutoLeftMatch"                                                    ∫                              xe2x80x83                            ⁢                                                ⅆ                  ω                                ⁢                                                      "LeftBracketingBar"                                                                  N                        ~                                            ⁡                                              (                        ω                        )                                                              "RightBracketingBar"                                    2                                                              ⁢                      "LeftBracketingBar"                                          N                ~                            ⁡                              (                ω                )                                      "RightBracketingBar"                              )        ,
wherein:
i=(xe2x88x921)xc2xd;
xcfx86(xcfx89) is a set of phases, more particularly a function which varies as a function of frequency;
{tilde over (P)}(xcfx89) is the frequency spectrum of a received signal;
Ñ(xcfx89) is the frequency spectrum of a noise component accompanying the received signal; and
{tilde over (F)}(xcfx89) is the frequency spectrum of the filtered signal, per the above equation.
Preferably, an embodiment the matched-phase noise filter includes an analog to digital converter (ADC) for receiving an analog composite, noise-dominated signal containing a signal of interest and for producing a digital composite signal, an input/output port receiving the digital composite signal and providing a matched-phase signal, and a processor receiving the digital composite signal via the I/O port and generating the matched-phase signal, wherein a signal to noise ratio between the signal of interest and a noise component within the digital composite signal is increased by approximately an order of magnitude, based on an actual spectrum of the digital composite signal and an estimated spectrum of the noise component and independent of the particular form of the signal of interest.
The present invention also encompasses a method for filtering a noise dominated signal. Preferably, the novel method includes the steps of:
producing an actual spectrum of the noise dominated signal responsive to the noise dominated signal;
selecting an estimated spectrum representing noise in the noise dominated signal; and
generating a desired spectrum indicative of a signal of interest based solely on the actual spectrum and the estimated spectrum and, thus, independent of the particular form of the signal of interest.
In accordance with a presently preferred embodiment, the method for filtering a noise dominated signal includes the steps of:
receiving a time series signal consisting mostly of noise and containing a signal of interest;
selecting a close estimate of the frequency dependence of the noise spectrum within the time series signal;
executing a Fast Fourier transform (FFT) of the time series signal so as to obtain spectral amplitudes and phases of each frequency component of the time series signal;
orthogonalizing the input spectral amplitude to the noise spectral amplitude so as to produce orthogonalized spectral amplitudes;
assigning phases to the resultant orthogonalized spectral amplitudes so as to produce assigned phases; and
inverse FFT transforming the assigned phases and the orthogonalized spectral amplitudes back into the time domain to thereby produce a matched-phase signal;
wherein a signal to noise ratio (SNR) of the signal of interest with respect to the noise in the matched-phase signal is at least an order of magnitude greater than the SNR of the time series signal.